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Reports (Research Report) Year : 2008

## Stability of Curvature Measures

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Frédéric Chazal
David Cohen-Steiner
• Function : Author
• PersonId : 833472
Boris Thibert

#### Abstract

We address the problem of curvature estimation from sampled compact sets. The main contribution is a stability result: we show that the gaussian, mean or anisotropic curvature measures of the offset of a compact set K with positive $\mu$-reach can be estimated by the same curvature measures of the offset of a compact set K' close to K in the Hausdorff sense. We show how these curvature measures can be computed for finite unions of balls. The curvature measures of the offset of a compact set with positive $\mu$-reach can thus be approximated by the curvature measures of the offset of a point-cloud sample. These results can also be interpreted as a framework for an effective and robust notion of curvature.
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### Dates and versions

inria-00344903 , version 1 (06-12-2008)

### Identifiers

• HAL Id : inria-00344903 , version 1
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### Cite

Frédéric Chazal, David Cohen-Steiner, André Lieutier, Boris Thibert. Stability of Curvature Measures. [Research Report] RR-6756, INRIA. 2008, pp.34. ⟨inria-00344903⟩

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